Lectures:
Naive set theory: operations on sets, relations between sets, and definition of these in terms of the 1st order predicate logic (FOL).
Cartezian product, relation, mapping (function).
Semantic methods in FOL.
Introduction to the thoery of formal proof calculi
Resolution method in propositional logic
General resolution in FOL; Robinson's unification algorithm
Natural deduction in propositional logic
Natural deduction in FOL
Soundness and Completeness of proof calculi
Presentation of the students' solution a given problem.
Theory of relations, types of relations, equivalence and ordering.
Algebraic theories, groups, rings and fields.
Theory of lattices, Formal Conceptual Analysis.
Formalized theories of arithmetic, Gödel's results (completeness and incompleteness)
Hilbert style proof calculi for propositional and predicate logic
Exercises:
Proofs of basic statements of the naive set theory.
Indirect proofs in propositional logic.
Resolution method in propositional logic.
The difference between relation and function, mathematical and empirical examples.
Proofs by semantic tableau in predicate logic.
Set-theoretical semantic proofs in predicate logic.
Traditional Aristoteles logic and the usage of Venn's diagrams.
Proofs of validness using the general resolution method.
Proofs of validness using natural deduction.
Proofs in the theory of relations and functions.
Proofs of basic theorems of arithmetic.
Projects:
Solving a given problem by natural deduction and resolution methods
Naive set theory: operations on sets, relations between sets, and definition of these in terms of the 1st order predicate logic (FOL).
Cartezian product, relation, mapping (function).
Semantic methods in FOL.
Introduction to the thoery of formal proof calculi
Resolution method in propositional logic
General resolution in FOL; Robinson's unification algorithm
Natural deduction in propositional logic
Natural deduction in FOL
Soundness and Completeness of proof calculi
Presentation of the students' solution a given problem.
Theory of relations, types of relations, equivalence and ordering.
Algebraic theories, groups, rings and fields.
Theory of lattices, Formal Conceptual Analysis.
Formalized theories of arithmetic, Gödel's results (completeness and incompleteness)
Hilbert style proof calculi for propositional and predicate logic
Exercises:
Proofs of basic statements of the naive set theory.
Indirect proofs in propositional logic.
Resolution method in propositional logic.
The difference between relation and function, mathematical and empirical examples.
Proofs by semantic tableau in predicate logic.
Set-theoretical semantic proofs in predicate logic.
Traditional Aristoteles logic and the usage of Venn's diagrams.
Proofs of validness using the general resolution method.
Proofs of validness using natural deduction.
Proofs in the theory of relations and functions.
Proofs of basic theorems of arithmetic.
Projects:
Solving a given problem by natural deduction and resolution methods